Position-Dependent Viscosity Effects on Rate Coefficients

Kramers's modeling of a chemical reaction by barrier-mediated diffusion is generalized to include a possible spatial variation of viscosity along the reaction coordinate. Expressions are derived for the rate coefficient $k$,$k$ is influenced by the viscosity at the location of the barrier top, which is partially affected by the solvent viscosity $\eta$. A predicted law $\delta \left(\ln k\right)=\epsilon \delta \left(\ln \eta \right)$ for $0<~\epsilon <~1$ is compatible with recent kinetic measurements in proteins.